A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. What is the width of this garden? A.) 12 cm B.) 10 cm C.) 10 in. D.) 12 sq. cm.

Question

Mathematics

Jaime James

5 August, 15:57

A rectangular garden has a perimeter of 48 cm and an area of 140 sq. cm. What is the width of this garden? A.) 12 cm B.) 10 cm C.) 10 in. D.) 12 sq. cm.

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Answers (1)

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Ayla Dawson · Answer 1

Perimeter: 2W + 2L = 48

Area = L x W = 140

Rewrite the area to solve for L: L = 140/W

Now replace that in the perimeter formula:

2W + 2 (140/W) = 48

Divide all terms by 2:

W + 140/W = 24

Divide both sides by W:

140 + w^2 = 24w

Subtract 24w from both sides:

w^2 - 24w + 140 = 0

Factor:

(w-10) (w-14) = 0

Solve for each w for 0:

10-10 - 10 and 14-14 = 0

So the 2 dimensions are 10 and 14 cm.

14 isn't a choice so the answer is B. 10 cm.